Axial force measuring method utilizing ultrasonic wave

ABSTRACT

A method of measuring axial force existing in a bolt or the like from two natural resonant frequency values of the bolt, the one of which being obtained when the axial force is zero under forced oscillation caused by an ultrasonic wave of a specific frequency, while the other being obtained when the axial force to be measured exists under forced oscillation caused by ultrasonic wave of the same frequency.

United States Patent [19 1 Makino et al.

[ Nov. 11, 1975 AXIAL FORCE MEASURING METHOD UTILIZING ULTRASONIC WAVEinventors: Takayukl Makino, Okazaki;

Haruhiko Toriyama. Toyota, both of Japan Toyota Jldosha Kogyo KabushikiKaisha, Toyota, Japan Filed: Mar. 29, 1974 Appl. No.: 456.285

Related U.S.. Application Data Continuation-impart of Ser. No. l96.896,N ov.' 9. i971. Pat. No. 3.822.587.

Assignee:

Foreign Application Priority Data Nov. 24. i970 Japan 45403555 US. Cl.73/67.2; 73/67.8 R; 73/88 F Int. Cl. GOlH 13/00; GOIL 5/12 Field ofSearch 73/67.2, 67.7, 67.8 R,

References Cited UNITED STATES PATENTS ll/l938 Nicolson 73/672 UX3.153.338 l0/l964 Kleesuttel 73/67.] 3.306.l00 2/1967 Wilhelm et al.73/672 FOREIGN PATENTS OR APPLICATIONS l.497,834 9/l967 France 73/88 FOTHER PUBLlCATlONS Ultrasonic Wave Velocity Changes with Stress,Ultrasonics, Apr.-June 1964. p. 95.

Primary Exnminen-RiChard C. Qucisser Assistant Examiner-John P.Beauchamp Attorney, Agent. or Firm-Stevens, Davis, Miller 84 Mosher [57]ABSTRACT 2 Claims, 7 Drawing Figures U.S. Patent Nov.11, 197s Sheet2of53,918,294

4 ton CORRESPOw/NG 3 AXIAL FORCE a a T4 llllll u w u n H M 5 n 0. n

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US. Patent Nov.11, 1975 Sheet3of5 3,918,294

FIG. 4

xuxmb wmk 5 tan AXIAL Fmcs U.S. Patent. Nov.11,1975 Sheet4of5 3,918,294

a N. QRQQ $533 3 a k$ Ax/AL FORCE AXIAL FORCE MEASURING METHOD UTILIZINGULTRASONIC WAVE CROSS REFERENCE TO RELATED APPLICATION This applicationis a continuation-in-part application? of our copending application Ser.No. l96896ftled on Nov. 9. 197i. now Pat. No. 3.822.587.

suM rt'v forfrrnz'trsviatsriors 2 said article is substantially zero;measuring a second naturalfrequency of said article when said article isunder strain andsaid axial force is greater than zero; determining theratio of change tfsr-fe lfm) between said first and second naturalfrequencies; and comparingthus determinedratio with calibrationdata-which hasbeen obtained'with'respect to axial force versus ratio ofchange; wherein the frequency of said ultra- This invention-relates toamethod ofrneasuring axialforcesiexisting iin the bolts or the-likeeasily and destructively by usingultrasonic waves. L

in the measurement of the axial forcesof boitsa' d the like. there hasgenerally been employed amethod sonic wave is such one as to satisfy theequation.

' (fikf ii/f t-Kl{(151 89' Vi +./(r-v.i\ r+,}-n, where-the symbolsrepresent the same as used in the statement of thefirst aspect oftheinvention.

in which the'axial force (0) oh bolt or the like t em mated from thetightening force (T) applied thereto.

However. such away of measuring is not reliable since the tighteningforce does not always represent the exact axial force.

There has also been employed a method in which the axial force of a boltor. the like is determined by measuring the amount of strain in thebolt,caused by the axial force, by means of a resistance wire strain'gauge.'This method is also disadvantageous in that this method v required sometest pieces which are drilled to provide for attachment of theresistance wire 'strpin gauge.

Recently. it has become avaiiable to;measure vthe axial force from thevalues of the natural resonant frequency of the bolt under forcedoscillation causedvby ultrasonic wave. Such'uitrasonic method issuperior in that the axial forcecan befmeasured easilyand mmdestructiveiy. a a v i v The present invention aims at providing anultrasonic method of measuring axial force whichmethodis im-" proved inthat it provides more accurate measuring when compared with conventionalultrasonic measuring method. 7

According to the invention. there is provided a method of obtaining ameasure of an axial forcelwithin an article under strain from avariation of natural frequencies of said article, comprising the stepsof: applying an ultrasonic wave to said article to generate forcedoscillations therein; measuring a first natural frequency of saidarticle when said axial force within said article is substantially zero;measuring a second natural frequency of said article when said articleis under strain and said axial force is greater than zero; determiningdifferential (fcr-fq) between said first and second nat uralfrequencies; and comparing thus determine'd dif-w ferentiai withcalibration data which has been obtained with respect to axial forceversus differential to locate The present invention will be described indetail hereinafter with reference to the accompanying drawings in which;

'FIG; I is a diagrammatical view illustrating the relationship betweenthe axial force and the tightening torque of a bolt or the like;

FIG. 2a is a diagram showing an example of a measuring circuit formeasuring the natural frequency of an article;

FIG. 2b is a diagram showing a current fluctuation in the-oscillationcircuit at the time of resonance;

FIG; 3 is a diagram exemplifying graphically the relationship betweenthe axial forces and the natural frequencies of a specific bolt for usein automobiles, es-

' tablished by selectively using two ultrasonic wave frequencies; I

FIG. 4 is a diagram graphically showing the relationship between axialforces and natural frequencies of a number of bolts for use inautomobiles, established by selectively using two ultrasonicfrequencies;

FIG.- 5-is a diagram graphically exemplifying the relationshipbetween'theaxial forces and the ratios of lation, 3 an ammeter forindicating the current l, flowing through the oscillation circuit, 4 anultrasonic wave the existing axial force; wherein the frequency of said1 ultrasonic wave is such one as'to satisfy the equation.

force within an article'under strain from a variation of naturalfrequencies of said article. comprising the steps of: applying anultrasonic wave to said article to generate forccd oscillations therein;measuring a first natural frequency of said article when said'axialforce within oscillator-consisting of crystal or barium titanateceramic.and 5 an article presented for the measuring. IWhenthe'oseillating wave generated by the oscillation circuit I is appliedto the ultrasonic wave oscillator it"toradiate the ultrasonic wave tothe article 5 and the oscillationfrequency is varied-by a variablecondenser cm the tuning circuit], the node and antinode of theoscillating wave are formed at predetermined positions in'the article asindicated by the dotted lines in FIG. 2.

Thus, when the frequency is such that the thickness 1 of the article andthe wavelength of the ultrasonic wave in said article are in a specificrelationship with each other. a simple harmonic motion occurs.

This simple harmonic motion is the natural tttiCiiilt tion of thearticle. and the natural frequency can be generaiiycalculated from thefollowing formula:

n-vlzr w'herefi's the natural frequency. [is the length of the bolts! isthe propagation speed in the article, and n is a positive integer.

and when n is equal to 2. 3. or 4. multiple frequency.

The natural frequency fthus sured in terms of a change of the currentvalue lp indi cated by the ammeter 3. as shdwn'in FlGL-2b.

Namely. when the oscillation frequency is gradually f represents'agenerated can befrnea Namely,-it

changed by the variable condenserCof the tuning circuit 2, resonanceoccurs in the article at the natural frequency fand the current lpincreases. I

Therefore. the basic frequency f and multiple frequcncies f,. f... .f,of the article can be readily read on a scale of the oscillationfrequency fc previously scaled relative to the capacity of the variablecondenser The basic frequency f aswili be understood from equatfionf(2)above, is represented by ln-I I and, therefore. can be determined bymeasuring adjacent two multiple frequencies.

The natural frequency 'f is generally given bythe equation (2). and. atthe same time is given by the following equation when the naturalfrequency is basic or fundamental one.

f-V/2l- VETS/:l-V'EW/t: wherein E is the Young's modulus;

p is the density,

M is the mass and V is the volume of the article.

Namely. it will be understood that the natural frequency fis in inverseproportion to the thickness 1 of the article and in proportion to thesquare root of the volume V and the Young's modulus of the same.

occurs an entirely unknown phenomenon that the frequency values fe. andfe=vary drastically according to thefr equency of the ultrasonic waveused in the measuring.

was noted that. while the actually meas'ured changing ratio well suitsto the theoretical relationship as defined by theequations 5 and 7 asfar as the frequency of ultrasonic wave used for measuring is lowerthansome' 2 m3 MHz. the measured changing ratio becomes muchgreater'than the theoretical value of changing ratio as obtained fromthe equations when the ultrasonic freq'uency used for measuring exceedsseveral MHz.

Thisnewly found out phenomenon will be explained with reference to FIG.3.

HO. 3 shows a representative example of the results ';0f the experimentsto seek the relationship between the axial force within a bolt andthenatural frequency of the bolt.

Twoultrasonic wave of different frequencies are employed, the one ofwhich being of 0.5 MHz while the other being of i0 MHz. The boltpresented for the experiment is 10 mm in diameter, 25 mm in length andabout 0.3 in Poisson's ratio.

ln.FlG. 3. the'axis of abscissa is scaled by axial force andthe axis ofordinate by natural frequency.

As'seen for the diagram, at the point where the axial force amounts to 5tons (The strain is calculated to be about 0.3% at this point). thenatural frequency changing ratio calculated from the measured naturalfrequency values amounts to 0.24% which value well suits I to thetheoretical value as obtained from the equation 6 when measured by theultrasonic wave of 0.5 MHz,

Now. a discussion will be made on thenatural frethe changinglalio that Pquency change resulting from occurrence of a strain in an article to bemeasured. When a load is exerted, for example, one cylindrical body tocause a tensile strain 1. the changing ratio of the natural frequenciesbefore .g used .Thus, when a constant'value K is defined as the ratio incase that the measuring'frequency of i0 MHz is between the actuallymeasured changing ratio and the and after the exertion of loadisrepresented by the fol-H 4 q calculated Ji 8 8 "lilo, when the lowingformula. provided that Young's modulus E and the mass M of thecylindrical body are constant:

value K is defined by 5o quency'of the ultrasonic wave employed in theSupposing that a tensile strain of 0.3% occurredin.

the cylindrical body,[the natural frequency changing ratio canbedetermined as follows based ontheloisson's ratio :1 0.3:

(fl-Lil];

and it will be seen that the natural frequency is lowered by 0.24% as aresult of occurrence of 0.3% vtensile strain.

Further, the changing ratio of the natural frequencies f. and f, in thecase of the strain being 1 (e, I g) a e. (a, 0) is respresented by thefollowing formula:

(f| --/nl/fs -{(lvs i vm/ (i-vm VH-nl-I 1) The inventors, during theprocess of'analyz ing the relationship between the actually measuredjchanging ratio of the natural frequencies and the changing ratiocalculated from above equation (7), found that there V [+0-003-l 4.0024(6i it is calculated that the K amounts to about.4.0 when measuring ismade by ultrasonic wave of 10 MHz, whereas Kis calculated to beabout l.0when thefremeasuringls 0.5MHz. v

in other words. the changing ratio of the natural frequency obtained byusing measuring frequency of i0 MHz is 5 times as great as thatobtainedby using meat suring frequency of 0.5 MHz.

T In order to confirm thisnewly foundout phenomenon. a furtherexperiment was conducted to seek the relationship between the changingratio (fq-fq/fe.) of

the. r|atural frequency and the varying measuring frequency. I

t Three bolts wcre presented for the experiment each one of'which beingl0.23 mm in effective diameter. 25

mm in length. 0.29 in Poisson's ratio and 2l000 itg/mm in Young'smodulus.

For each bolt, natural frequencies (T1,) was meazero by using aboveultrasonic waves.

The natural frequencies fs, andfe, thus measured was then calculated toobtain thechanging ratio (fa,- fqlfe as summarized in Tablel.

Thus. ifit is intended to locate the existing axial force by comparingmeasured difference (fa -[6,) or meatsured changing ratio Lferfq/fq)with the calibration data which has been obtained with respect to axialTABLEl 7 Measuring Frequency w l MHz 3 MHz ft' I'l or f r-f lms fir'f lf l f's f s bolt Axial KHz x i0 K": 'x i0" Force (Ten) 0 ll2.42 0 H583 0i 2 li2.26 l.42 5.66 2.J3 4 a ll2.ll 2.76 ll$.37 -4.83 0, il2.30 0ll5.78 0 2 2 ll2.l$ l.34 ll$.53 -2.l6

4 ll2.0l 2.S8 ll$.24 -4.66 0 ll2.08 0 ,ll$.52 0 3 2 lll.97 0.98 5.28-2.08 4 lll.8l 2.4l il5.02 -4.33 4 MHz 5 MHz 8 MHz f f r f'l orfw-fq/fs. or fq-fq/fs, or fq-fn/fs. s fs f s KHz x i0" KH: 1 It) KHz xi0" No.78 0 116.75 0 6.70 0 H638 -34} ll6.37 -3.25 6.30 3.43 llo.04-6.34 No.02 6.25 5.98 6.l7 ll6.55 0 H653 O H6.Sl 0 ll61i7 4.26 ll6.l63.l8 ll6.l3 -3.27 l 15.85 -6.0l ll$.82 6.09 l l5.82 5.92 ll6.25 0 M622 0ll6.22 0 ll5.8ti -3.i8 il5.86 -3.l0 llS.87 3.0l ll5.57 -$.85 H563 -5.94il$.$5 -$.25

The diagram of FIG. 6, which. is plotted in accordance with the valuesof Table I, shows that whenthe measuring frequency exceeds 4 MHz, thechanging ratios are almost constant for varying measuring frequenciesand are averaged at 0.61% when the axial force is 4 tons and at 0.32%when the axial force is 2mm, respectively.

force versus difference or axial force versus changing ratio,respectively, the axial force can be located more exactly when abovespecific measuring frequency is used in comparison with the case whererelatively low measuring frequency, say 0.5 MHz, is used.

.Those skilled in the art would easily understand that the-larger thedifference or the changing ratio becomes,

The theoretical values of the changing ratio in turn 1 the more accuratemeasuring can be expected.

FIG. 5 shows a graphrepresenting the relationship between the varyingaxial force and the frequency changing ratio. a The'graph in FIG. 5 wasobtained in the following manner.

pieces of ring gear setting bolts for vehicles were presented for thetest.

As described above, when a'specific frequency is emw ployed for themeasuring, the measured changing ratio large as the theoretical value.

Although this newly found out phenomenon, which has been confirmedthrough many experiments, has not been theoretically developed yet', itis true that axial forces can be measured more accurately when this 50.of natural frequency. well reaches more than 4 tim'e sas newly found outphenomenonis positively utilized in the measuring. H Namely, if themeasuring were conducted using-an ultrasonic wave of such frequency astomake the value ents the value of changing ratio close to thetheoretical value.

of K in the equation (8) greater than 3. the difference" Thefirst'natural frequency (i.e. fe.) was measured for each bolt at zeroforce using an ultrasonic wave of 10 MHz.

Then thesecond naturalfrequencies (i.e. fq) were measured bythe samemeasuring frequency and where the axial force is l, 2, 3, 4 and 5 tonsrespectively for each bolt. The axial forces were read from a tensiletestor.

.Then the frequency changing ratio (i.e. fe -fi m.) was calculated withrespect to each axial force for each bolt.

The upper and lower curve show the upper and lower extremes offluctuation among 50 measurements.

it will be understood that the changing ratio decreases steeply as theaxial force increases, so that one can exactly locate the existing axialforce by comparing measured changing ratio with the data on the curve ofFlG.;5 when itis utilized as a calibration curve.

Although aboveexplanation was made with respect to 'a method in whichthe, measured changing ratio is compared (with the calibration datawhich has been force. it is fairly possible to use a calibration datawhich concerns the difference (fe -fq) versus axialforce. In. the lattercase, natural frequency (fe,) atzero'forceand natural frequency-(fe,).at. ;loaded .conditionyare mea sured using an ultrasonic-wave ofafrequency. fore'x ample l MHz.'and then the difference fla -feyis.calculatedto be compared with the calibratio'n'data.

it will be understood'that. when suchspecific rneasuring frequency asmakesthe value of K'in'the equa;. tion (8) larger than 3. forexample"lO'MHa alarger" value of the difference can beobtained for achange in and this entirely owes to the newly found out phenomenon.

axial force comparing with the case where relatively];

low measuring frequency. for example 0.5 MHz. as will be seen from FlG.3,

Thus, by comparing the measured difference with'the tightened;

calibration data'which' are drawn with respect toithe difference versusaxial force. one can know the existing' axial force more exactly thanthe casewhere relatively low measuring frequency is used. and thisentirely owes to the newly found out phenomenon of the present in-'vention.

The above explanation was made withrespect to the cases where thenatural frequency of thebolt at zero force can be measured. v

Apart from above. the present invention is also applicable to the caseswhere the natural frequency of the bolt at zero force cannot bemeasured.

in other words. the present invention enables .it to. measure the axialforce of the bolt at tightened'condition without loosening it, asdescribed hereunder with reference to H0. 4.

FIG. 4 shows by way of example the relationships between the axial forceand the natural frequency, actually measured on 50 ring gear settingbolts for automobiles by usin'g ultrasonic frequencies of about 0.5MHz-' and about 10 MHz. The vertical axis represents the naturalfrequency, while the abscissa indicates the readings of the tensiletester or any otherconventional means which can indicate the axial forcewithin the article. a

in the diagram. characters A and B represent the data measured by usingultrasonic waves of frequencies of about 10 MHz and 0.5 MHzrespectively. and character C represents a graph obtained by subtractingthe data of B from the data of A. in each of the A. B and C. the data ofthree representative bolts X. Y and 2 located at the upper limit, themiddle portion and the lower limit thereof are indicated by O, X andrespectively.

it is considered that the fiuetuatio'ns which occur among measuredvalues of several articles. such as'the values of X. Y and Z. isattributable to the irregularities in length. heat-treating conditionsand concentrations of ingredients of the bolt. it is observed that thefluctuation. i.e. the deviation from the mean or standard value iscommon for all measuring frequencies.

Therefore, by drawing a graph by plotting'the differlt'wili be obviouslyunderstood that'by measuring the natural frequencies of a bolt by usingthe two ultrasonic wavesof frequencies o'f'about 10 MHz and 0.5 MHz.caiculatingthe difference between the measured values of naturalfrequencies and-comparing" the calculated difference with a calibrationcurve previously drawn on the bolt with respect to axial force versusthe difference. the'vaiueof the axial force within the bolt can bereadily obtained;

Thus. the axial force of the bolt can be readily, accurately. simply andnon-destructively determined in its assembled state without thenecessity of previously measuring the natural frequency of the boltbefore it is --Al though the foregoing description has been given on amethod of determining the axialforce of a bolt or the likebym'easuring-the natural frequencies thereof, it will be understood thatmeasuring the propagation time has exactly thesamesigniiicance as thatof measuring the natural frequency, because the reciprocatingpropagation time T of ultrasonic wave in a bolt or the like can beexpressed by the following formula:

T-Zl/V- l/(VlZlil/f (9) Namely, the axial force of a bolt or the likecan of course be determined by measuring the reciprocating time ofultrasonic wave in the bolt or the like, i.e. the period from theultrasonic wave is projected from one end of the bolt or the like to thetime when it returns to said end upon reflecting at the other end. byusing. for example, an ultrasonic reflectroscope.

As described herein in detail, the method of the present inventionprovides, simple. highly accurate and non-destructive measuring of theaxial force existing within articles.

' What is claimed is:

. l. Amethod ofobtaining a measure of an axial force -3--within anarticle under strain from a variation of naturalfrequencies ofjsaidarticle. comprising the steps of:

applying an ultrasonic wave to said article to generate forcedoscillations therein; measuring a first natural frequency of saidarticle when said axial force within said "article is substantiallyzero'. measuring a second natural frequency of said article when saidarticle is under strain and said axial force is greater than zero;

' determining differential (fag-Is between said first and second naturalfrequencies; and comparing thus determined differential with calibrationdata which has been obtained .with respect toaxial force versusdifferential to locate th e existing axial force: the frequency of saidultrasonic wave being selected to satisfy the equation. tju-lmlfcieKlit-xm {Tim-w.) {miiwhere fei is the first measured natural frequency ofsaid article when'the strainthereof is s. (or; 0),fs is the encesbetween the values obtained by usingrthe ultra- J sonic wave ofafrequency of about 10 MHz and the values obtained 'by using theultrasonic wave of a frequency of about 015 MHz.on each bolt. thefiu ctuation the fluctuation promising: more accuratejmeasuring.

second measured natural frequency of said article when the'strai nthereof is qte, O). K is a constant greater than 3. arid v is Poissonsratio.

2. A method of obtaining a measure of an axial forceWithinanarticIe-untier strain from a variation of natural frequencies ofsaid article. comprising the steps of: applying an ultrasonic wave tosaid article to generate forced oscillations therein; measuring a firstnatural frequency of said'article when said axial force within saidarticle is substantially zero; measuring a second natural frequency ofsaid article when said article is under strain and said axial force isgreater than zero;

10 where fa, is the first measured natural frequency of said articlewhen the strain thereof is a (e, z 0),fe, is the second measured naturalfrequency of said article when the strain thereof is e, (e, 0), K is aconstant greater than 3, and v is Poisson's ratio.

1. A method of obtaining a measure of an axial force within an articleunder strain from a variation of natural frequencies of said article,comprising the steps of: applying an ultrasonic wave to said article togenerate forced oscillations therein; measuring a first naturalfrequency of said article when said axial force within said article issubstantially zero; measuring a second natural frequency of said articlewhen said article is under strain and said axial force is greater thanzero; determining differential (f Epsilon 2-f Epsilon 1) between saidfirst and second natural frequencies; and comparing thus determineddifferential with calibration data which has been obtained with respectto axial force versus differential to locate the existing axial force;the frequency of said ultrasonic wave being selected to satisfy theequation, (f Epsilon 2-f Epsilon 1)/f Epsilon 1 K(((1- Nu Epsilon 2)square root 1+ Epsilon 1/ (1- Nu Epsilon 1) square root 1+ Epsilon 2 )-1), where f Epsilon 1 is the first measured natural frequency of saidarticle when the strain thereof is Epsilon 1 ( Epsilon 1 > OR = 0), fEpsilon 2 is the second measured natural frequency of said article whenthe strain thereof is Epsilon 2 ( Epsilon 2 > 0), K is a constantgreater than 3, and Nu is Poisson''s ratio.
 2. A method of obtaining ameasure of an axial force within an article under strain from avariation of natural frequencies of said article, comprising the stepsof: applying an ultrasonic wave to said article to generate forcedoscillations therein; measuring a first natural frequency of saidarticle when said axial force within said article is substantially zero;measuring a second natural frequency of said article when said articleis under strain and said axial force is greater than zero; determiningthe ratio of change (f epsilon 2-f epsilon 1/f epsilon 1) between saidfirst and second natural frequencies; and comparing thus determinedratio with calibration data which has been obtained with respect toaxial force versus ratio of change; the frequency of said ultrasonicwave being selected to satisfy the equation, (f epsilon 2-f epsilon 1)/fepsilon 1 K(((1- Nu epsilon 2) Square Root 1+ epsilon 1/ (1- Nuepsilon 1) Square Root 1+ epsilon 2)-1) where f epsilon 1 is the firstmeasured natural frequency of said article when the strain thereof isepsilon 1 ( epsilon 1 > or = 0), f epsilon 2 is the second measurednatural frequency of said article when the strain thereof is epsilon 2 (epsilon 2 > 0), K is a constant greater than 3, and Nu is Poisson''sratio.